Uncertainty Quantification for Stochastic Nonlinear Systems using Perron-Frobenius Operator and Karhunen-Lo'eve Expansion

Abstract : In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using Karhunen-Lo'eve (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty evolution in a Duffing oscillator and a Vanderpol's oscillator. It is observed that the solution of the approximated stochastic dynamics converges to the true solution in distribution. Finally, the proposed methodology is combined with Bayesian inference to estimate states of a nonlinear dynamical system, and its performance is compared with particle filter. The proposed estimator was found to be computationally superior than the particle filter.
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Submitted on : Monday, October 15, 2012 - 4:14:36 PM
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Parikshit Dutta, Abhishek Halder, Raktim Bhattacharya. Uncertainty Quantification for Stochastic Nonlinear Systems using Perron-Frobenius Operator and Karhunen-Lo'eve Expansion. CCA - IEEE International Conference on Control and Applications, IEEE Control Systems Society, Oct 2012, Dubrovnik, Croatia. pp.1449-1454, ⟨10.1109/CCA.2012.6402455⟩. ⟨hal-00741997⟩

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